Some orchid types can be cut back to encourage reblooms (such as Phalenopsis or Phal., although it's never a sure thing) and many cannot. They simply do their thing once a year and when it's over you wait a season.
If yours is a Phal. or the related Dtps. genus, you can cut the flower spike back and wait and see. Be sure the leaves look healthy though. Flowering can tax the plant, and prolonged flowering can cause it to suck the energy it needs to bloom from the leaves. That can 'suicide' a weak plant.
If your plant is a Phal, and the leaves look good, look up the flower spike. There are numerous joints, or 'nodes'. The first several are close up to the spike and no flowers grew out of them. After the non-blooming nodes, you'll come to the ones where the flowers emerged, but have since dropped off. Cut the spike between the last non-blooming node and the first flowering node. Then wait.
If the spike will rebloom, you should see new growth branching off just below your cut sometime in the next month. If nothing appears, I'd cut the spike close to the plant, and let the plant put its engery into making new roots and leaves - which will give you a stronger flowering cycle next year.